To simplify \((c^2 d^3)^{-\frac{1}{3}}\), follow these steps:

1. **Apply the Negative Exponent Rule**:  
   \((a^m)^{-n} = \frac{1}{(a^m)^n}\).  
   So,
   \[
   (c^2 d^3)^{-\frac{1}{3}} = \frac{1}{(c^2 d^3)^{\frac{1}{3}}}
   \]

2. **Distribute the Exponent**:  
   Apply the exponent \(\frac{1}{3}\) to each term inside the parentheses separately:
   \[
   \frac{1}{(c^2)^{\frac{1}{3}} \cdot (d^3)^{\frac{1}{3}}}
   \]

3. **Simplify Each Term**:
   - For \(c^2\), apply the power rule \((a^m)^n = a^{mn}\):
     \[
     (c^2)^{\frac{1}{3}} = c^{\frac{2}{3}}
     \]
   - For \(d^3\), apply the same rule:
     \[
     (d^3)^{\frac{1}{3}} = d^1 = d
     \]

4. **Combine the Results**:
   \[
   \frac{1}{c^{\frac{2}{3}} \cdot d}
   \]

So, the final simplified expression is:
\[
\boxed{\frac{1}{c^{\frac{2}{3}} d}}
\]

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:
1. How would you simplify \((a^4 b^2)^{\frac{1}{2}}\)?
2. What is the result of \((x^3 y^6)^{\frac{1}{3}}\)?
3. Can you simplify \((m^5 n^{-2})^{\frac{1}{5}}\)?
4. How do you expand and simplify \((p^2 q^3)^{-\frac{2}{3}}\)?
5. What does \((x^2 y^4 z^3)^{\frac{1}{2}}\) simplify to?

**Tip:** When simplifying expressions with exponents, make sure to apply the exponent to each factor inside the parentheses individually.

Learn how to simplify the expression (c^2 d^3)^(-1/3) with a detailed step-by-step solution. This problem involves applying the negative exponent rule and power rule for exponents, covering key algebraic concepts. Suitable for students in Grades 7-9.

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